David,
Since you have an equation which involves a transcendental
function, it is almost always impossible to find a closed
form solution involving x only.
At this point one needs to resort to numerical techniques.
Here you can use FindRoot[f(x) == 0, {x,x0}]. For example,
FindRoot[10*Log[x] + 2*x - 3 == 0,{x,4},
WorkingPrecision -> 30]
would yield,
x = 1.0862...(to thirty places)
Note that I would recommend plotting the function over a range
of x. Obviously here, x must be > 0, and plotting will help
you to see the zeros of the function. Have fun
Wilson.
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